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Pushing a box stuck to the ground at discrete locations

Pushing a box stuck to the ground at discrete locations

Pushing a box stuck to the ground at discrete locations

(OP)
I have a rigid box. It is stuck to the ground with scotch tape at discrete locations around the box. I would like to determine the forces developed at the scotch tape locations when I push and pull on the box with forces F1 and F2.

Assume I know all the geometric information about this experiment. This would include the length, width and height of the box, the relative location of application of the forces F1 and F2 and locations of the scotch tape.

Assume also that the box and ground are fairly rigid with respect to the scotch tape.

What simple analytical method exists to solve a problem like this?


RE: Pushing a box stuck to the ground at discrete locations

If F2 is applied at the centroid of the box / tape arrangement then F2/# of connections.

The shear at the tape would be F1/# of connections that can resist the load (may only be 4 in this case).

The uplift would be F1*distance of force from the ground/ moment arm of connections.

RE: Pushing a box stuck to the ground at discrete locations

(OP)
structSU10, a couple of comments:

"If F2 is applied at the centroid of the box / tape arrangement then F2/# of connections."

Sure, that makes sense.

"The shear at the tape would be F1/# of connections that can resist the load (may only be 4 in this case)."

I contest the fact that only 4 connections are activated to resist the load. To me it looks like all of them are resisting the shear load. Could you please provide more basis for the fact that only 4 are activated, and which ones in particular?


"The uplift would be F1*distance of force from the ground/ moment arm of connections."

Does this include all connections or only a few? Please elaborate.

RE: Pushing a box stuck to the ground at discrete locations

I would be inclined to say only 4 would resist the shear because the tape is flexible and stretchable. So the only ones that would really contribute to the shear resistance would be the 4 that are parallel to the load direction.

For the moment resistance, all pieces of tape would contribute, except the ones on the face of the box where the load is applied.

RE: Pushing a box stuck to the ground at discrete locations

(OP)
Is there a more rigorous (numerical or analytical) method to come up with these forces? All the assumptions stated so far are great but I'm looking for a more general and scientific method to determine the reactions.

RE: Pushing a box stuck to the ground at discrete locations

It's time to let the cat out of the bag and tell us what the real problem is as opposed to saying a box taped to the ground.

RE: Pushing a box stuck to the ground at discrete locations

A general solution is what you're already gotten.
A scientific method involves you getting a box, some scotch tape, and figuring out what happens. A great example of this is the shear question - Like SU10 & jayrod, I suspect that the tape parallel to the load will resist the load, but not the tape perpendicular to the load, but test it!
Regarding the overturning, it will be a combination of the tape acting in tension and the box bearing in compression. How may pieces of tape act will act in tension and the length of the compression zone is up to you, but assuming an elastic distribution, you'll have 4 pieces of tape in tension, and half the perimeter/area in compression, depending on whether or not the box has a bottom and how rigid it is.

RE: Pushing a box stuck to the ground at discrete locations

I would direct you to the Mythbusters television program which tested duct tape used in various loading configurations. They were pretty rigorous if not analytical.

RE: Pushing a box stuck to the ground at discrete locations

(OP)
Once2003, The reason structSU10's suggestion is not general can be illustrated by the following modification to the above system:

Say we remove the 4 anchors on the side which supposedly resist shear. If the loads remain the same, what now resists the shear? I guess what I'm getting at by "general solution" is somthing that can give me reactions for any arrangement of "scotch tape" or loading. Thanks...

RE: Pushing a box stuck to the ground at discrete locations

Sounds like you need to call 3M

RE: Pushing a box stuck to the ground at discrete locations

The solution of the reactions with a rigid box and perfect tape should be pretty easy assuming perfect load sharing etc to avoid a statically indeterminate situation.

As other said, What each piece of tape thinks of this is far from certain as the loading is likely quite different.
https://images-na.ssl-images-amazon.com/images/G/0...
If the load exceeds the peel strength, then that piece of tape will cease to contribute much.
Except possibly x-rays,
http://www.foxnews.com/story/2008/10/23/peeling-sc...
in turn making the experiment fall under NRV regulations.
http://www.nrc.gov/reading-rm/doc-collections/cfr/...

I think The contribution of the 4 tapes shown left in the 16:31 post are especially troublesome, as it looks like pure peeling from one surface or another. Those would likely quite weak, making the solution of the actual reactions that more difficult.

RE: Pushing a box stuck to the ground at discrete locations

Awa5114:
It’ll never work. You can’t push something like that with a chain. Whoops..., the chain thing wasn’t supposed to come to light until the 60th guess/post. Is it double strength scotch tape or the cheap stuff which doesn’t stick to ‘the ground?’ Your wish for rigorousity in your analysis is only surpassed by your ignorancety in presenting your problemexity. Never, never present the real problem when you can complexify the whole discussion significantly by leaving out 90% of the important engineering details. You are a hell of a long way from resolving any engineering problem when you can’t define it with some engineering specificity.

The simple answer is...., there is no simple answer, there is no simple analytical method which exists to solve a problem like this. They used to call it Statics and Engineering Mechanics which you should have learned in college. Try it out, what assumptions do you have to make to get it to work, to get a solution, a first approx? Essentially the things you said you know in your OP, except you don’t know these things and you haven’t spelled them out. Then they threw in Strength of Materials, Theory of Elasticity, simple structures and indeterminate structures, still pretty simple and clean the way they taught them. Finally you get out in the real world, and behold..., the simple text book diagrams and problem presentations and the all encompassing formulations intended to explain one specific issue or idea no longer fit the bill, because a hundred real world realities enter the picture, and screw up your basic assumptions.

You say you “know all the geometric information about this experiment” and “Assume also that the box and ground are fairly rigid with respect to the scotch tape,” and at the same time you don’t know a damn thing, and haven’t spelled any of it out for us. So, if we want to waste more time at our boss’ expense we/some of us keep guessing at what you want. Thus, the comment, ‘let the cat out of the bag, what’s the real problem?’ You might generalize how you start to approach or think about a problem like this based on your education and experience, but you quickly start to see that some things overpower the approach you must take for a real solution. And, I’m not sure you can write a general enough formula to cover it all. And, sometimes you have to make some simplifying assumptions, some changes, do some experimenting to further the thought process and solution. For example..., if the box is 1' high and 1' wide, but 30' long (front to back, your OP picture); or if the box is 30' high and 1' x 1' in plan; or if there are only 4 pcs. of take (one each side) vs. 10 or 12 pcs. of tape; would you approach the problem the same way and/or get the same results? Some of the general thinking would apply, but the exact formulation and approach, would of necessity, be different. “Fairly rigid” means almost nothing without a whole bunch more knowledge about the various components. Are the box sides stiff enough as a beam so they stay essentially straight (no deflection) as one end lifts and the other is pressed down to the ground? Because of the ways tape would take the loads and the variables it introduces to the problem, it must be the worst choice for this connection feature that you could possibly imagine. The tape adhesive bond plane to the box is mostly loaded in shear and it is capable in that loading mode. It is much less capable in peeling as it is lifted off the ground (table top surface?) due to the various loads. The tape isn’t much good at distributing/transmitting a shearing force in its plane or around the 90̊ corner (box to table top) since it can buckle and start peeling, neither of which are easy to define or formulate.

It might be o.k. to broach a problem like your O.P. in a face to face discussion, because I would quickly start questioning your approach and assumptions and eliminate 75 or the first 100 suspect issues fairly quickly. But, to try to do that here, on E-Tips, where we are just playing a guessing game and wasting our time is a futile effort. Either clear up some of the details and answer some of the questions that have been asked, and maybe rephrase and reorganize your question (O.P.) or quit wasting our time.

RE: Pushing a box stuck to the ground at discrete locations

(OP)
Allright. The real problem is that I am trying to calculate required loading/stress for HVAC equipment anchorage. F1 and F2 are simply horizontal and vertical components of seismic loading per ASCE 7 chapter 13. I thought I could dumb it down to a simple problem like this because every resource I've seen on the subject talks only about design code requirements but does not provide an answer to the real question: How do we determine the loads on the anchors? We get plenty of stuff on how to determine capacities, etc, but proper structural analysis to determine loading on the anchors? Zero.

RE: Pushing a box stuck to the ground at discrete locations

Awa5114:
Dumbing it down either says something about the guy asking the question or his respect for the intelligence of people he is asking for help, and neither of these is very good. Don’t do that, it leads to trouble and confusion, and makes you look dumb. Explain your real problem, and with enough real engineering details, dimensions, loads and facts so we can have a meaningful engineering discussion. You would be surprised what an experienced engineer can glean about and understand about a real problem when given all the important engineering info. We get no shortage of dumb/stupid questions here on E-Tips, without people dumbing it down for the fun of it. It could not have been more difficult for you to start this thread with your very last post, at least the people offering help would have known where you were coming from, because we have all done these types of problems dozens of times. This is generally an indeterminate problem which depends on the stiffness of the equipment itself; and then depends on the stiffness of the skid/frame on which the equip. is mounted, and finally on the stiffness of the beams or framing just above the roof, part of the building structure, onto which the equip. skid is finally bolted/welded. You have immediately eliminated the biggest confusion (100 variables & questions), the damn tape. Now, you are saying you have fairly rigid connections, all able to take vert. loads and global moments, but some stiffer in transmitting shear loads (horiz. loads) in one direction or the other, and still ultimately dependant on the stiffness of the various elements in the entire system. You could use some 3D frame analysis software to analyze the whole system to find the reactions, and that my be educational given your question. Usually, some simplifying assumptions are made, and simple statics and the AISC code do the trick.

RE: Pushing a box stuck to the ground at discrete locations

I still think that my previous assumption is how I would design the anchorage anyway. Assuming the anchorage is as per you first post I would assume the anchors on the sides parallel to the lateral force resist the shear. And the other anchors resist the uplift from overturning.

Too many variables at play otherwise. It results in overdesigned anchorage but considering the overall project cost, slightly overdesigned anchorage is just a drop in the 5 gallon bucket.

RE: Pushing a box stuck to the ground at discrete locations

Jayrod12:
I agree with your approach completely, per my last sentence above. Up sizing the bolts a size or adding a couple more bolts, is not worth your analysis time in most cases. The issue that I’d like to drive home is that dumbing down the problem or question.... ‘a box, taped to the ground???’ invariably adds more confusion than clarity, and invariably leads to a game of 20 questions, not a meaningful engineering discussion. Explain your problem in ‘engineering speak,’ with enough detail so we can understand and visualize it, and let the help/discussion begin.

RE: Pushing a box stuck to the ground at discrete locations

dhengr,

Agreed whole-heartedly. I didn't feel the need to rub it in to the OP.

RE: Pushing a box stuck to the ground at discrete locations

(OP)
Hey Jayrod, quick question. With the assumptions stated above (ie anchor points not tape), doesn't this reduce down to an internal shear/moment problem? What I mean is a problem requiring the use of internal stress equations like My/I and VQ/It or ones similar to them? The system can be idealized as a "quasi cantilevered" beam with fixed base. The beam is just short and fat like a box.

I got this idea from looking at the following video: https://www.youtube.com/watch?v=YpDEnL8TjrM

The lecturer uses a modified (My/I)+(P/A) equation for discrete points. It is modified as follows:

tension/compression per anchor = (My/(Sum(d^2))+(P/(no anchors))

He does however use a simplification for the resulting shear

Shear per anchor = V/(no anchors)

I don't like this simplification. If we are using analogues to My/I and P/A for moment and axial, should we not also use an analogue to VQ/IT for shear? If so what could this analogue be? the problem would be the thickness to use... since for a beam we use the beam thickness, but for a set of discrete anchor bolts there's no real "thickness" to use, but maybe there is a way to simplify this equation for shear to make the responding shear loads quasi-parabolic (which is what they should be, in my opinion).

RE: Pushing a box stuck to the ground at discrete locations

Oh you probably can. But those calculations to save you some on the anchorage likely will cost the same amount in fees compared to my assumptions.

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